UCSC-SOE-14-10: Flexible Integro-Difference Equation Modeling for Spatio-Temporal Data

Robert Richardson, Athanasios Kottas and Bruno Sanso
09/11/2014 08:21 AM
Applied Mathematics & Statistics
The choice of kernel in an integro-difference equation (IDE) approach to model spatio-temporal data is studied. By using approximations to stochastic partial differential equations, it is shown that higher order cumulants and tail behavior of the kernel affect how an IDE process evolves over time. The asymmetric Laplace and the family of stable distributions are presented as alternatives to the Gaussian kernel. The asymmetric Laplace has an extra parameter controlling skewness, whereas the class of stable distributions includes parameters controlling both tail behavior and skewness. Simulations show that failing to account for kernel shape may lead to poor predictions from the model. For an illustration with real data, we consider ozone pressure measurements collected biweekly by radiosonde at varying altitudes. We compare the results obtained with the different kernel families and confirm that better model prediction may be achieved by electing to use a more flexible kernel.

Paper revised on July 24, 2016.